Accurate and efficient <i>a posteriori</i> account of geometrical imperfections in Koiter finite element analysis

Garcea, Giovanni; Liguori, Francesco S.; Leonetti, Leonardo; Magisano, Domenico; Madeo, Antonio

doi:10.1002/nme.5550

Cited by 45 publications

(46 citation statements)

References 46 publications

(69 reference statements)

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“…15 Unfortunately, they suffer from numerical locking or mesh sensitivity. 16,17 The solution to the problem has so far been either to employ a much more refined mesh than that used for conventional buckling analysis to evaluate the IPBCs or to employ specially formulated elements, [18][19][20][21][22][23] none being an attractive option.…”

Section: The Concept Of Full Commutativity and Apparent Symmetrymentioning

confidence: 99%

Commutativity of the strain energy density expression for the benefit of the FEM implementation of Koiter's initial postbuckling theory

Yan

Zhang

et al. 2018

Numerical Meth Engineering

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Summary The concept of full commutativity of displacements in the expression for strain energy density for the geometrically nonlinear problem has been introduced for the first time and fully established in this paper. Its consequences for the FEM formulation have been demonstrated. As a result, the strain energy, equilibrium equation, and incremental equilibrium equation for the geometrically nonlinear problem can all be presented in a unified manner involving various stiffness matrices that are all symmetric, unique, and explicitly expressed. As an important application, the framework has been employed in the FEM implementation of Koiter's initial postbuckling theory, which has been handicapped by its mesh sensitivity in evaluating one of the initial postbuckling coefficients. This has largely prevented it from being incorporated in mainstream commercial FEM codes. Based on the outcomes of this paper, the mesh sensitivity problem has been completely resolved without the need to use any specially formulated element. As a result, Koiter's theory can be practically and straightforwardly implemented in any FEM code. The results have been verified against those found in the literature.

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Section: The Concept Of Full Commutativity and Apparent Symmetrymentioning

confidence: 99%

Commutativity of the strain energy density expression for the benefit of the FEM implementation of Koiter's initial postbuckling theory

Yan

Zhang

et al. 2018

Numerical Meth Engineering

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“…with , , and  being still to be determined, linear, quadratic, and cubic forms. Using (7) and (11) in the equilibrium (5) and equating the coefficients of the various powers of to zero results in the following 3 linear relations:…”

Section: Construction Of the Reduced-order Modelmentioning

confidence: 99%

“…In the following, we present a concise summary of the construction of the reduced-order model and the global equilibrium solution. A detailed summary revealing the relations between the higher-order forms of (5) and (11) and the derived systems of equations can be found in Liang et al 12 :…”

Section: Construction Of the Reduced-order Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The method reduces the large number of equations needed to model accurately the elastic buckling behavior of shells to a few nonlinear equations representing the modal amplitudes and the load factor of the deformed structure. 10,11 Recently, a novel Koiter-Newton approach has demonstrated successfully a reliable and accurate prediction of the buckling phenomena of thin-walled structures. [12][13][14] The main idea of this approach is the use of Koiter's method as a nonlinear predictor within the framework of a path-following strategy.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An efficient mixed variational reduced‐order model formulation for nonlinear analyses of elastic shells

Magisano

Liang

Garcea

et al. 2017

Numerical Meth Engineering

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Summary The Koiter‐Newton method had recently demonstrated a superior performance for nonlinear analyses of structures, compared to traditional path‐following strategies. The method follows a predictor‐corrector scheme to trace the entire equilibrium path. During a predictor step, a reduced‐order model is constructed based on Koiter's asymptotic postbuckling theory that is followed by a Newton iteration in the corrector phase to regain the equilibrium of forces. In this manuscript, we introduce a robust mixed solid‐shell formulation to further enhance the efficiency of stability analyses in various aspects. We show that a Hellinger‐Reissner variational formulation facilitates the reduced‐order model construction omitting an expensive evaluation of the inherent fourth‐order derivatives of the strain energy. We demonstrate that extremely large step sizes with a reasonable out‐of‐balance residual can be obtained with substantial impact on the total number of steps needed to trace the complete equilibrium path. More importantly, the numerical effort of the corrector phase involving a Newton iteration of the full‐order model is drastically reduced thus revealing the true strength of the proposed formulation. We study a number of problems from engineering and compare the results to the conventional approach in order to highlight the gain in numerical efficiency for stability problems.

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Nonlinear Thermal Buckling Analysis of Thin‐walled Structures: Solid‐shell Discretization, Continuation Method and Reduction Technique

et al. 2022

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This work presents an accurate and efficient numerical tool for geometrically nonlinear thermoelastic analyses of thin‐walled structures. The structure is discretized by an isogeometric solid‐shell model with an accurate approximation of geometry and kinematics avoiding the parameterization of finite rotations. An efficient modeling of thermal strains, temperature‐dependent materials and general temperature profiles based on a numerical pre‐integration through the shell thickness is proposed. Then, a generalized path‐following method is developed for solving the discrete equations with the temperature amplifier as additional unknown, in order to trace the temperature‐displacement nonlinear curve also in case of limit points and unstable paths. A consistent definition of the tangent operators and a mixed integration point strategy give a robust and efficient analysis. Finally, a reduction technique is derived for a quick estimate of the nonlinear thermal buckling point. The reduced model consists of the initial path tangent, the first linearized buckling modes and their second order corrections. Numerical applications are given.

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Accurate and efficient a posteriori account of geometrical imperfections in Koiter finite element analysis

Cited by 45 publications

References 46 publications

Commutativity of the strain energy density expression for the benefit of the FEM implementation of Koiter's initial postbuckling theory

Commutativity of the strain energy density expression for the benefit of the FEM implementation of Koiter's initial postbuckling theory

An efficient mixed variational reduced‐order model formulation for nonlinear analyses of elastic shells

Nonlinear Thermal Buckling Analysis of Thin‐walled Structures: Solid‐shell Discretization, Continuation Method and Reduction Technique

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